Question

if `tan theta = 12/5` find the value of `(1 + sin theta)/(1 -sin theta)` 

Answer 1

Given `tan theta = 12/5`

We have to find the value of the expression  `(1 + sin theta)/(1 -sin theta)`

From the above figure, we have

`AC = sqrt((AB)^2 +  (BC)^2)`

`= sqrt(12^2 + 5^2)`

=  13

`=> sin theta = 12/13`

Therefore

`(1 +sin theta)/(1 + sin theta) = (1 + 12/13)/(1 - 12/13)`

= 25

Hence, the value of the given expression is 25